Question: Find an equation for the line, in the indicated form, with the given properties. Containing the points: $(1,0)$ and $(2,3)$. General Form
1. **State the problem:** Find the equation of the line passing through the points $(1,0)$ and $(2,3)$ in general form.
2. **Recall the formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Calculate the slope:**
$$m = \frac{3 - 0}{2 - 1} = \frac{3}{1} = 3$$
4. **Use point-slope form:**
The equation of the line using point-slope form is
$$y - y_1 = m(x - x_1)$$
Using point $(1,0)$:
$$y - 0 = 3(x - 1)$$
$$y = 3x - 3$$
5. **Convert to general form:**
General form is $Ax + By + C = 0$.
Rearranging:
$$y = 3x - 3$$
$$-3x + y + 3 = 0$$
6. **Final answer:**
$$\boxed{-3x + y + 3 = 0}$$
This is the equation of the line in general form passing through the points $(1,0)$ and $(2,3)$.